Swapping Coordinates

Pick any function, and list a subset of its set of ordered pairs. If you switch the x and y coordinates for every ordered pair in this subset, is the new result (called the inverse of the original function) also function? Try this process again for other functions.
Is the new result, or inverse, always a function? Explain.

Extension:
Graph the reversed coordinates. How does the graph of the original function relate to this new graph, and is this relationship the same for the graphs of all functions and their inverses? Explain.